What is the derivative of (x^4+6x-1)/(7x^2-6x+1) ?

The derivative of (x^4+6x-1)/(7x^2-6x+1) is (14x^5-18x^4+4x^3-42x^2+14x)/((7x^2-6x+1)^2)

What is the first derivative of (x^4+6x-1)/(7x^2-6x+1) ?

The first derivative of (x^4+6x-1)/(7x^2-6x+1) is (14x^5-18x^4+4x^3-42x^2+14x)/((7x^2-6x+1)^2)

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derivative of

\frac{x ^{4} + 6 x - 1}{7 x ^{2} - 6 x + 1}

\frac{14 x ^{5} - 18 x ^{4} + 4 x ^{3} - 42 x ^{2} + 14 x}{( 7 x ^{2} - 6 x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{4} + 6 x - 1}{7 x ^{2} - 6 x + 1})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{4} + 6 x - 1 ) ( 7 x ^{2} - 6 x + 1 ) - \frac{d}{d x} ( 7 x ^{2} - 6 x + 1 ) ( x ^{4} + 6 x - 1 )}{( 7 x ^{2} - 6 x + 1 ) ^{2}}

\frac{d}{d x} (x^{4} + 6 x - 1) = 4 x^{3} + 6

\frac{d}{d x} (7 x^{2} - 6 x + 1) = 14 x - 6

= \frac{( 4 x ^{3} + 6 ) ( 7 x ^{2} - 6 x + 1 ) - ( 14 x - 6 ) ( x ^{4} + 6 x - 1 )}{( 7 x ^{2} - 6 x + 1 ) ^{2}}

Expand

(4 x^{3} + 6) (7 x^{2} - 6 x + 1) - (14 x - 6) (x^{4} + 6 x - 1) : 14 x^{5} - 18 x^{4} + 4 x^{3} - 42 x^{2} + 14 x

= \frac{14 x ^{5} - 18 x ^{4} + 4 x ^{3} - 42 x ^{2} + 14 x}{( 7 x ^{2} - 6 x + 1 ) ^{2}}

sin (15 x)

\int 6 - x^{2} d x

y^{^{'}} = \frac{1 - y ^{2}}{t}

f (x) = 4 x^{2} + 2 x, (- 2, 12)

\int \frac{x ^{7}}{2} - \frac{1}{x ^{5}} d x

What is the derivative of (x^4+6x-1)/(7x^2-6x+1) ?
The derivative of (x^4+6x-1)/(7x^2-6x+1) is (14x^5-18x^4+4x^3-42x^2+14x)/((7x^2-6x+1)^2)
What is the first derivative of (x^4+6x-1)/(7x^2-6x+1) ?
The first derivative of (x^4+6x-1)/(7x^2-6x+1) is (14x^5-18x^4+4x^3-42x^2+14x)/((7x^2-6x+1)^2)